On some percolation results of J. M. Hammersley
- 1 June 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (03) , 526-540
- https://doi.org/10.1017/s0021900200107673
Abstract
We examine how much classical percolation theory on lattices can be extended to arbitrary graphs or even clutters of subsets of a finite set. In the process we get new short proofs of some theorems of J. M. Hammersley. The FKG inequality is used to get an upper bound for the percolation probability and we also derive a lower bound. In each case we characterise when these bounds are attained.Keywords
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